The use of a partially simulated exothermic reactor to test nonlinear algorithms

Two nonlinear control algorithms for controlling nonlinear systems include the receding horizon method and the nonlinear neural network inverse model methods. These methods have been found to be useful in dealing with difficult-to-control nonlinear systems, especially in simulated systems. However although much simulation work has been performed with these methods, simulation only is inadequate to guarantee that these algorithms could be successfully implemented in real plants. For this reason, a relatively low cost and simple online experimental configuration of a partially simulated continuous reactor has been devised which allows for the realistic testing of a wide range of nonlinear estimation and control techniques i.e. receding horizon control and neural network inverse model control methods. The results show that these methods are viable and attractive nonlinear methods for real-time application in chemical reactor systems.     

The control of MSF desalination plants based on inverse model control by neural network

In this paper, a nonlinear inverse model control strategy based on neural network is proposed for MSF desalination plant. Artificial neural networks (ANNs) can handle complex and nonlinear process relationships, and are robust to noisy data. The designed neural networks consist of three layers identified from input–output data and trained with a descent gradient algorithm. The set point tracking performance of the proposed method was studied when the disturbance is present in the MSF system. Three controllers are designed for controlling the top brine temperature, the level of last stage and salinity. These results show that a neural network inverse model control strategy (NNINVMC) is robust and highly promising to be implemented in such nonlinear systems. Also the comparison between the top brine temperature of the proposed model and NN predicted data from the literature supports the accuracy of the model.     

Neural‐Networks‐Based Feedback Linearization versus Model Predictive Control of Continuous Alcoholic Fermentation Process

In this work advanced nonlinear neural networks based control system design algorithms are adopted to control a mechanistic model for an ethanol fermentation process. The process model equations for such systems are highly nonlinear. A neural network strategy has been implemented in this work for capturing the dynamics of the mechanistic model for the fermentation process. The neural network achieved has been validated against the mechanistic model. Two neural network based nonlinear control strategies have also been adopted using the model identified. The performance of the feedback linearization technique was compared to neural network model predictive control in terms of stability and set point tracking capabilities. Under servo conditions, the feedback linearization algorithm gave comparable tracking and stability. The feedback linearization controller achieved the control target faster than the model predictive one but with vigorous and sudden controller moves.     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

Modeling, simulation and control of a methanol synthesis fixed-bed reactor

In this paper, the dynamic behavior and control of the low pressure methanol synthesis fixed bed reactor have been investigated. For simulation purpose, a heterogeneous one-dimensional model has been developed. First, the reactor simulation is carried out under steady-state condition and the effects of several parameters such as shell temperature, feed composition (especially CO₂ concentration) and recycle ratio on the methanol productivity and reactor temperature profile are investigated. Using the steady state model and a trained feedforward neural network that calculates the effectiveness factor, an optimizer which maximizes the reactor yield has been developed. Through the dynamic simulation, the system open loop response has been obtained and the process dynamic is approximated by a simple model. This model is used for the PID controller tuning and the performances of fixed and adaptive PID controllers are compared for load rejection and set point tracking. Finally the proposed optimizer is coupled with a controller for online optimization and hot spot temperature protection.     

Trajectory tracking of a batch polymerization reactor based on input–output-linearization of a neural process model

Input–output-linearization via state feedback offers the potential to serve as a practical and systematic design methodology for nonlinear control systems. Nevertheless, its widespread use is delayed due to the fact that developing an accurate plant model based on physical principles is often too costly and time consuming. Data-based modeling of dynamic systems using neural networks offers a cost-effective alternative. This work describes the methodology of input–output-linearization using neural process models and gives an extended simulative case study of its application to trajectory tracking of a batch polymerization reactor.     

工业渣油催化裂化过程六集总组合反应器模型

工业渣油催化裂化反应主要发生在提升管段和出口的沉降器段的复杂流体动力学区域。通过对工业现场装置流程和过程数据的分析,将发生裂化反应的整个反应器中提升管部分作为活塞流反应器(PFR)和沉降器部分作为全混流反应器(CSTR)的串联组合反应器,并按照渣油催化裂化反应特点建立了简化的6集总组分的串行和并行动力学反应网络模型。所建立的稳态催化裂化反应产率预测模型在数学上表现为提升管部分的微分方程组和沉降器部分的代数方程组。模型设置7个装置因数来校正模型的计算产率与实测产率之间的偏差,并采用工业现场数据回归装置因数。通过对工业装置数据的计算比较,得到的模型产率预测精度很好地满足在线软测量计算要求。     

基于动态补偿逆的非线性RBF内模控制及其应用

针对非线性不确定系统和传统的非线性内模控制在控制上存在的不足,提出一种基于动态补偿逆的非线性不确定系统RBF内模控制,在引入RBF建立逆模型的同时,将无模型自适应控制方法作为附加控制器,用于模型偏离被控对象时在线修正逆模型。仿真结果表明,本文提出的方法不仅对系统的常量摄动具有较好的鲁棒性,对时变不确定性仍然保持较好的跟踪效果,具有较好的实时性、鲁棒性和在线校正功能。     

基于复合神经网络的离散非线性系统建模与控制

An adaptive inverse controller for nonliear discrete-time system is proposed in this paper. A compound neural network is constructed to identify the nonlinear system, which includes a linear part to approximate the nonlinear system and a recurrent neural network to minimize the difference between the linear model and the real nonlinear system. Because the current control input is not included in the input vector of recurrent neural network (RNN), the inverse control law can be calculated directly. This scheme can be used in real-time nonlinear single-input single-output (SISO) and multi-input multi-output (MIMO) system control with less computation work. Simulation studies have shown that this scheme is simple and affects good control accuracy and robustness.     

典型大时变时滞系统神经网络模糊PID控制及应用

针对典型大时变时滞系统,设计了一种基于神经网络的模糊PID控制器.该控制器综合模糊逻辑、神经网络与PID调节的各自优点,既具有模糊控制简单和有效的非线性控制作用,又具有神经网络的学习和适应能力,同时还具备PID控制的广泛适应性.该控制器能实现系统参数大范围失配情况下的闭环鲁棒稳定,并使闭环系统达到设定值无静差跟踪及满意的动态性能.     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network,AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

基于小波神经网络的通用模型控制

针对通用模型控制要求被控对象有显式解的局限性,应用小波神经网络来建立非线性被控对象的逆模型.再结合通用模型控制算法,将非线性过程模型直接嵌入到控制器中,来实现对被控对象的逆控制.其参考轨迹是一条典型的二阶曲线,控制器参数具有明显的物理意义,且易于整定.仿真结果验证了该控制策略的有效性.     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.     

Generalized delta rule (GDR) algorithm with generalized predictive control (GPC) for optimum temperature tracking of batch polymerization

The generalized delta rule (GDR) algorithm with generalized predictive control (GPC) control was implemented experimentally to track the temperature on a set point in a batch, jacketed polymerization reactor. An equation for optimal temperature was obtained by using co-state Hamiltonian and model equations. To track the calculated optimal temperature profiles, controller used should act smoothly and precisely as much as possible. Experimental application was achieved to obtain the desired comparison. In the design of this control system, the reactor filled with styrene-toluene mixture is considered as a heat exchanger. When the reactor is heated by means of an immersed heater, cooling water is passed through the reactor-cooling jacket. So the cooling water absorbs the heat given out by the heater. If this is taken into consideration, this reactor can be considered to be continuous in terms of energy. When such a mixing chamber was used as a polymer reactor with defined values of heat input and cooling flow rate, system can reach the steady-state condition. The heat released during the reaction was accepted as a disturbance for the heat exchanger. Heat input from the immersed heater is chosen as a manipulated variable. The neural network model based on the relation between the reactor temperature and heat input to the reactor is used. The performance results of GDR with GPC were compared with the results obtained by using nonlinear GPC with NARMAX model.The reactor temperature closely follows the optimal trajectory. And then molecular weight, experimental conversion and chain lengths are obtained for GDR with GPC.     

CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR BY WIENER INPUT/OUTPUT DATA-BASED PREDICTIVE CONTROLLER WITH DIRECT INVERSE IDENTIFICATION

This article reports an experimental study for the identification and predictive control of a continuous methyl methacrylate (MMA) solution polymerization reactor. The Wiener model was introduced to identify the polymerization reactor in a more efficient manner than the conventional methods of Wiener model identification. In particular, the method of subspace identification was employed and the inverse of the nonlinear part was directly identified. The input variables in this work were the jacket inlet temperature and the feed flow rate, while the monomer conversion and the weight average molecular weight were selected as the output variables. On the basis of the identified model a Wiener-type input/output data-based predictive controller was designed and applied to the property control of polymer product in the continuous MMA polymerization reactor by conducting an on-line digital control experiment with online densitometer and viscometer. Despite the complex and nonlinear characteristics of the polymerization reactor, the proposed controller was found to perform satisfactorily for property control in the multiple-input multiple-output system with input constraints for both set-point tracking and disturbance rejection. This was also confirmed by simulation results.     

CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR BY WIENER INPUT/OUTPUT DATA-BASED PREDICTIVE CONTROLLER WITH DIRECT INVERSE IDENTIFICATION

This article reports an experimental study for the identification and predictive control of a continuous methyl methacrylate (MMA) solution polymerization reactor. The Wiener model was introduced to identify the polymerization reactor in a more efficient manner than the conventional methods of Wiener model identification. In particular, the method of subspace identification was employed and the inverse of the nonlinear part was directly identified. The input variables in this work were the jacket inlet temperature and the feed flow rate, while the monomer conversion and the weight average molecular weight were selected as the output variables. On the basis of the identified model a Wiener-type input/output data-based predictive controller was designed and applied to the property control of polymer product in the continuous MMA polymerization reactor by conducting an on-line digital control experiment with online densitometer and viscometer. Despite the complex and nonlinear characteristics of the polymerization reactor, the proposed controller was found to perform satisfactorily for property control in the multiple-input multiple-output system with input constraints for both set-point tracking and disturbance rejection. This was also confirmed by simulation results.     

Perturbation signal design for neural network based identification of multivariable nonlinear systems

The paper focuses on issues in experimental design for identification of nonlinear multivariable systems. Perturbation signal design is analyzed for a hybrid model structure consisting of linear and neural network structures. Input signals, designed to minimize the effects of nonlinearities during the linear model identification for the multivariable case, have been proposed and its properties have been theoretically established. The superiority of the proposed perturbation signal and the hybrid model has been demonstrated through extensive cross validations. The utility of the obtained models for control has also been proved through a case study involving MPC of a nonlinear multivariable neutralization plant.     

NONLINEAR HEAT EXCHANGER CONTROL THROUGH THE USE OF PARTIALLY LINEARIZED CONTROL VARIABLES

The use of partial linearization by nonlinear state variable feedback has been proposed as a means of reducing the detrimental effects of system nonlinearities upon the performance of linear control schemes used with nonlinear systems. In this paper a set of generalized transformed variables are derived for a single pass shell and tube heat exchanger using this technique. The implementation of these generalized transformed variables, which reduce the apparent nonlinear behavior of single pass heat exchangers, eliminates the need to rederive a nonlinear transformation for each heat exchanger controller design. As shown by open loop transient behavior of the system, the transformed variables reduce the nonlinear characteristics of the system response. The closed loop performance of the heat exchanger system has been evaluated for both servo and regulator control, and the effect of model error upon the robustness of the closed loop controller performance has been investigated.     

Modelling and control of different types of polymerization processes using neural networks technique: A review

Polymerization process can be classified as a nonlinear type process since it exhibits a dynamic behaviour throughout the process. Therefore, it is highly complicated to obtain an accurate mechanistic model from the nonlinear process. This predicament always been a “wall” to researchers to be able to devise an optimal process model and control scheme for such a system. Neural networks have succeeded the other modelling and control methods especially in coping with nonlinear process due to their very conciliate characteristics. These characteristics are further explained in this work. The predicament that is encountered by researchers nowadays is lack of data which consequently lead to an imprecise mechanistic model that scarcely conforms to the desired process. The implementations of the neural network model not only restrict to polymerization reactor but to other difficult‐to‐measure parameters such as polymer quality, polymer melts index and mixture of initiators. This work is aimed to manifest ascendancy of neural networks in modelling and control of polymerization process.     

Nonlinear internal model control strategy for neural network models

A nonlinear internal model control (NIMC) strategy based on neural network models is proposed for SISO processes. The neural network model is identified from input—output data using a three-layer feedforward network trained with a conjugate gradient algorithm. The NIMC controller consists of a model inverse controller and a robustness filter with a single tuning parameter. The proposed strategy includes time delay compensation in the form of a Smith predictor and ensures offset-free performance. Extensions for measured disturbances are also presented. The NIMC approach is currently restricted to processes with stable inverses. Two alternative implementations of the control law are discussed and simulations results for a continuous stirred tank reactor and pH neutralization process are presented. The results for these two highly-nonlinear processes demonstrate the ability of the new strategy to outperform conventional PID control.